Theorems · Theorem · field theory
Polynomial.monic_multisetProd_X_sub_C
∀ {R : Type u} [inst : CommRing R] (s : Multiset R),
(Multiset.map (fun a => Polynomial.X - Polynomial.C a) s).prod.Monic- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.mapstatement · cited by 876
- Multiset.prodstatement · cited by 528
- Polynomial.Monicstatement · cited by 461
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.monic_multiset_prod_of_monicproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_Cproof · cited by 3
- Polynomial.exists_prod_multiset_X_sub_C_mulproof · cited by 1
- max_norm_root_eq_spectralValueproof · cited by 1